Let's say you have two rollouts of exactly the same checker play and you
used the same rollout parameters. Both use a random seed. One was for
500 games, and one was for 1000 games.
Can you combine the results, weighting the 1000 game rollout result
double the 500 game rollout and get the equivalent of a 1500 game
rollout? Or does this just 'dilute' the more accurate 1000 game rollout
with the less accurate 500 game rollout?
Gregg C.

Yes, the two rollouts combined are exactly the same as a standard 1500
trial rollout, with one tiny caveat: There is a teensy chance that the
"random seed" will end up being the same random seed for both trials,
in which case you still only have 1000 trials worth of information. But
the odds of that are so small that I wouldn't worry about it.
You have one rollout with equity E1 and standard deviation S1 after T1
trials, and a second rollout with E2, S2, T2. To combine them into one
big happy combined rollout EC, SC, TC you use, ignoring the "n-1"
adjustment for standard deviations:
TC = T1+T2
EC = (E1*T1 + E2*T2)/TC
SC = sqrt( (S1^2*T1^2 + S2^2*T2^2 + T1*E1^2 + T2*E2^2) / TC^2 - EC^2 / TC )